The BBC runs headlines of articles that have quotation marks used in ways that perplex me. They don't seem to show a literal sense (Clint Eastwood: "Make my day") or a figurative sense (Italian PM attacked "out of the blue") of their contents. The only commonality seems that they usually surround the predicate of the headline, but the headlines read perfectly fine without them. Can anyone explain their usage?

It does read perfectly fine without the quotes, but I think it says something different. Without the quotes, it would be the BBC stating that Iranians had siezed the oil well. To me, the quotes indicate that they are just repeating a statement by Iranian officials, which may or may not be true.
Iranian troops "take control of Iraqi Oil well" (at least, that's what the Iranians are saying)

This habit of the BBC's web writers is difficult to understand. I presume that sometimes they are quoting someone without direct attribution, but this does not explain why they do it when the facts described within quotation marks are unquestionable and do not need to be signalled as being opinions or unchecked assertions (which the BBC should not be basing its news stories on in any case).

The practice makes it appear as though the BBC has no confidence in its own reporting, or that it is suggesting that its sources are not to be trusted. Regardless, it is highly irritating and even patronizing.

It also reminds me of the equally annoying habit that some people have of giving capitals For No Real Reason to Certain Words they feel are Particularly Important.

On a related matter, I've noticed that American headline writers more often than not capitalize almost every word, such as in this headline from today's New York Times: A Race to Win One More Vote for Health Bill.

Why they think this is desirable or necessary is something I don't understand either.

The "stalker" one seems okay to me. The Associated Press article's headline reads "Alleged Jennifer Garner stalker in custody".
I have to admit I was wondering why James Garner would have a stalker. ;-)

.. with the use quotation marks I would suggest that there is some level of legal advice in there too .. by using the quotation marks, even without direct attribution, they have distanced themselves from any direct legal action .. it is in the same vein as one of my pet peeves with editors who insist on using the adjective "alleged" even when the criminal has been found with their hand on the axe handle with the axe firmly embedded in the victims head and witnessed by 10 policemen to have committed the murder .. the crime is still only "alleged" to have happened ..

I can see that argument potentially applying to stories that involve parties or events with British connections, but I don't see it with a story like "Iranian troops 'take control of Iraqi oil well' ", where it seems inconceivable to me that the BBC could have anything to fear from libel lawyers. Also, the BBC puts things in quotation marks where there is no implied or alleged improper behaviour or infraction of the law (e.g. "India 'has fewer Kashmir troops' ").

.. Edwin at last a person who speaks the true tongue .. I only call them quotation marks so that the newspeak yanks can understand my posts .. to the educated they will always be inverted comas .. (WoZ feeling his tongue slip from his cheek.) ..

Erik said:

Also, the BBC puts things in quotation marks where there is no implied or alleged improper behaviour or infraction of the law (e.g. "India 'has fewer Kashmir troops' ").

.. Erik here, to me, it is not a matter of legal worries but pure and simply a question of not being able to be said to be wrong .. quitely obviously when it turns out (hypothetically) that there are in fact more Kashmir troops then the journalist, who has zilch research skills and was only looking for a sensational headline anyway, can point the finger and hold the pretext that it was his "source" and not the journalist that got it wrong and his "reputation" as a truthful journalist remains in tact .. yeah right !! ..